Cool that you're a mathematician and computer scientist! That is totally out of my realm
As for your proposal... yes I would support it. In fact, I would say that ownership of cars would not even be necessary if a good transport system could be designed that is disseminated enough to allow a wide range of transport. Unless of course one is going to the country or off the beaten path, but even they could link their car with the automated driving network to get reasonable far.
The fossil fuel industry really did a number on efficient transportation infrastructure in North America. The city I'm living in now, Vancouver, used to have a wide range trolly system all over the city, but it got replaced with paved roads once it was felt that fuelled cars were the future. Gas companies and car companies gave substantial endorsements to city counsellors and that changed the whole game, forever.
Imagine how much fuel we could save with an automated driving network.